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13 May, 17:07

A spring-powered dart gun is unstretched and has a spring constant 16.0 N/m. The spring is compressed by 8.0 cm and a 5.0 gram projectile is placed in the gun. The kinetic energy of the projectile when it is shot from the gun is

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  1. 13 May, 17:10
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    Given that,

    Spring constant = 16N/m

    Extension of spring

    x = 8cm = 0.08m

    Mass

    m = 5g = 5/1000 = 0.005 kg

    The ball will leave with a speed that makes its kinetic energy equal to the potential energy of the compressed spring.

    So, Using conservation of energy

    Energy in spring is converted to kinectic energy

    So, Ux = K. E

    Ux = ½ kx²

    Then,

    Ux = ½ * 16 * 0.08m²

    Ux = 0.64 J

    Since, K. E = Ux

    K. E = 0.64 J
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